An old Wash U alumn (political science primary major, business second major and economic minor) and T14 admit here as merely an “above average” student with very strong LSATs.
First off, “prestige” won’t matter when you’re comparing two schools of this caliber when it comes to law school admissions. What will matter is the work you do when you go to either of these schools. Admissions officers, law firms and people hiring at large corporations, ie those who matter, know both schools well. 25 years ago a partner named best in finance in his MBA class (also a JD) at Northwestern looked at my CV and said, “I never could have gotten in there for undergrad”. That was when WashU’s name was much less known than it is today. I would not worry about name recognition for either.
Secondly, I’m not sure that Georgetown is more prestigious. Someone else brought up the grad school peer assessment rankings. If this was a large public program, those may not translate well to the undergrad program and the professors and research driving those rankings may have little to do with undergrad Ed. At WashU (and presumably Georgetown) those professors are actively teaching/mentoring undergrads. I would not say that WashU has any sort of advantage due to rankings, because again, when you get to schools/programs of this level, it frankly no longer matters.
Georgetown will offer greater breadth with respect to political science, economics, public policy, international affairs and government. That’s their jam. WashU only mints about 160 bachelors degrees a year total in those fields. Georgetown: 4 times as many. At the same time, you can only take so many of those courses in a 120 credit hour undergrad career. You’ll need distribution requirements and the opportunity to try things. Those create a more well rounded grad regardless. There’s no shortage of quality courses to build an academic resume at either school.
One thing in WashU’s favor: if you’re interested in examining law with a political science lens, WashU may be as good as any school in the country to do that. Lee Epstein is my favorite professor of all time and a great human being. She’s also probably the foremost expert in the world on judicial behavior and the politics of the judicial nominee process. She would probably also cringe if people said that last sentence. But it’s true. Her in class lectures (as opposed to her presentations around the world) are a nice balance between Con Law + historical context/psychology, lecture segments with Socratic bursts. She’s wonderful.
Andrew Martin was a protege of hers getting his PhD when I was an undergrad. Excellent in his own right. He was Martin in the Martin-Quinn scores (Google it) and an excellent empirical legal study scholar. He’s now Chancellor. Legal studies within the political science department is one of the university’s pride and joys. That’s not changing with him in charge of the entire university. He still teaches as well. Those two + James Gibson, Matt Gabel and James Spriggs are probably 5 of the 15-20 or so most cited political scientists in the US who fall under the broad category of “judicial politics”. Look them up in Google scholar. WashU is probably as strong as any school in the country in that niche. I think Penn may be up there as well. Google scholar still has Epstein at USC Law. She’s been back at WashU a number of years. There are some interesting cross disciplinary courses that weren’t there when I was in school and also some interesting strands (South Asian politics and social movements for example)
I don’t know the Econ side as well. They did have some interesting profs who focused on regulatory/institutional economics (led by Doug North). I enjoyed Andy Sobel’s classes on international regulatory frameworks that fell more under the “political economy” label. He’s still there.
A lot of words to say that it is a very good mix of professors passionate about teaching. Very good all around and completely exceptional in some areas like judicial politics/behavior. Professors got to know people well and the environment was extremely collaborative.
I really wouldn’t sweat perceptions of programs/universities from the general public. The people you’re trying to impress for admissions and jobs already know both well. I’d pick the school you think you will have the most personal happiness, because that translates to academic performance and general well being far more than hairsplitting advantages/disadvantages re: curriculum and rep.